Dirac solutions for quaternionic potentials

Abstract

The Dirac equation is solved for quaternionic potentials, i V0 + j W0 (\documentclass[12pt]{minimal}\begin{document}$V_{{0}}\in \mathbb {R}\,,\,\,W_{{0}}\in \mathbb {C}$\end{document}V0∈R,W0∈C). The study shows two different solutions. The first one contains particle and anti-particle solutions and leads to the diffusion, tunneling, and Klein energy zones. The standard solution is recovered taking the complex limit of this solution. The second solution, which does not have a complex counterpart, can be seen as a V0-antiparticle or |W0|-particle solution.